On the Number of Representations of One as the Sum of Unit Fractions

The Egyptian Fractions of One problem (EFO), asks the following question: Given a positive integer n, how many ways can 1 be expressed as the sum of n non-increasing unit fractions? In this paper, we verify a result concerning the EFO problem for n=8, and show the computational complexity of the problem can be severely lessened by new theorems concerning the structure of solutions to the EFO problem.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2019

Author dc:creator

• Crawford, Matthew Brendan

Chair dc:contributor.committeechair

• Palsson, Eyvindur Ari

Committee members dc:contributor.committeemember

• Mendelson, Samuel
• Orr, Daniel D.

• Egyptian Fraction
• Unit Fraction
• Combinatorics
• Number Theory

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:20999

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/90573